Understanding additive and multiplicative structures: the effect of number structure and nature of quantities on primary school students' performance

Abstract

The present study explores relationships between additive and multiplicative structures in the context of proportional reasoning. One goal is to examine hypothetical learning trajectories derived from these relations in the context of understanding proportionality. 198 Spanish primary school children were given a test which involved twelve problems with proportional and non-proportional situations in which the relationship between quantities (integer or non-integer) and the nature of quantities (discrete or continuous) were manipulated. Findings revealed the existence of two separate additive and multiplicative structures and that the integer and non-integer relationships between quantities play different roles in these two structures. In additive situations, understanding the integer relationship between quantities was a forerunner to success while in the proportional situations the important thing was to understand non-integer relationships between quantities.